GCF of 2016/318, 2036/518
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2016/318, 2036/518 i.e 4/82362 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2016/318, 2036/518.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 2016/318,2036/518?
Given fractions are 2016/318,2036/518
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 2016/318,2036/518, numerators are 2016,2036
Denominators are 318,518
The GCF of 2016,2036 is 4 .
LCM of 318,518 is 82362.
The greatest common factor of 2016/318,2036/518 = [GCF of 2016,2036]/[LCM of 318,518]= 4/82362
Therefore, the GCF of 2016/318,2036/518 is 4/82362.
To find the highest common factor of 2016,2036, we have to find the factors of both numbers and list the highest common factor.
The factors of 2016 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016
The factors of 2036 are 1, 2, 4, 509, 1018, 2036
The HCF of 2016,2036 is 4.
Lets's calculate GCF of 2016,2036
| 2 | 2016, 2036 |
| 2 | 1008, 1018 |
| 504, 509 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 2016,2036 By Matching Biggest Common Factor Method
Now, list down the factors of 2016
:1,2,3,4,6,7,8,9,12,14,16,18,21,24,28,32,36,42,48,56,63,72,84,96,112,126,144,168,224,252,288,336,504,672,1008,2016
Now, list down the factors of 2036
:1,2,4,509,1018,2036
Greatest Common Factor
We found the factors 2016,2036 . The biggest common factor number is the GCF number.
So the greatest common factor 2016,2036 is 4.
Lets's calculate LCM of 318,518
| 2 | 318, 518 |
| 159, 259 |
∴ So the LCM of the given numbers is 2 x 159 x 259 = 82362
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/82362
Therefore, the GCF of Fractions 2016/318,2036/518 is 4/82362
Least Common Multiple of 318,518 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 318,518 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(318,518) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(318,518) x common factors =2 x 1 = 2
LCM(318,518) = ( 318 × 518 ) / 2
LCM(318,518) = 164724 / 2
LCM(318,518) = 82362
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FAQs on GCF of Fractions of 2016/318, 2036/518
1. What is the HCF of 2016,2036?
The HCF of 2016,2036 is 4
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 2016/318, 2036/518?
Answer: GCF of Numerators as per given numbers 2016/318, 2036/518 is
GCF of Numerators i.e. for 2016,2036 is 4
LCM of denominators i.e. for 318,518 is 82362.
Thus, GCF of Fractions is 4/82362.Finally, GCF of Fractions for 2016/318, 2036/518 is 4/82362.